# Eg does not equal W = Ek

1. Oct 20, 2011

### anonymous12

1. The problem statement, all variables and given/known data
For our Work-Energy lab, we are supposed to prove that W = Eg = Ek but no matter what I do, my Eg doesnt not equal the Ek = W.

In this lab, we had a tray dangling via a string which is attached to a cart which is on a dynamic track made out of platinum. We let go of the cart (start the stop watch) and when the cart hits the metal beam (we stop the stop watch). We calculated the ∆h by measuring initial height - final height. What am I doing wrong in my calculations?

mass of cart: 0.25468g
∆t = 1.03
mass of tray = .0199kg
∆h = .488m
∆d = 0.5m
a = .94m/s^2
vf = 0.9682m/s

2. Relevant equations
Eg = mgh
Ek = .5mv^2

3. The attempt at a solution
Eg = .0199 x 9.8 x .488
Eg = 0.95J

Ek = 0.5 x .25468 x (0.9682)^2
Ek = 0.119J

W = a x m x ∆d
= .94 x .25468 x .5
= 0.119J

According to the Law of conservation of energy, Ek, Eg and W should equal each other or be very close to each other but no matter what, I can't get them to equal each other.

2. Oct 20, 2011

### PeterO

Due to the inability of a human to operate a stop watch very well, it is an unsuitable instrument for measuring times less than 5 seconds with any precision.

You will only start the watch withing 0.1 sec of when you intended (at best) and will only stop it within 0.1 sec as well.
Thus any time you measure will be ± 0.2 seconds at best.
The time interval you are using about 1 second so you have a 20% uncertainty.
Indeed you probably only get times within 0.2 at start and finish so 40% uncertainty is almost assured.
Trends would seem to be the best you can hope for.

3. Oct 20, 2011

### PeterO

I think one of the "=" signs [in red above] is supposed to be a "+" sign???

It is not actually clear to me how you are performing this experiment, and what you have measured??????